How to calculate Standard error of mean as shown in minitab website

Hi, I trying to recreate the minitab formula(so that I can use it in Matlab) for calculating standard error of mean as shown in this link Step 2 ( http://support.minitab.com/en-us/minitab-express/1/help-and-how-to/modeling-statistics/anova/how-to/two-way-anova/interpret-the-results/key-results/ ). However, I am unable to get the answer as shown on the web ? is there anyone who knows how ?

Answer 1

[Star Strider]

The Minitab site doesn’t show the calculation, so I assume it’s the usual definition:

data = rand(1, 10);
SEM = std(data)/sqrt(length(data));                             % Standard Error Of The Mean

[crixus]

hi thanks for your reply, I have tried this but unable to get the same answer as what's shown on minitab page. Example their sintertime at 20.3333, 21.4444 and 20.2222. My standard error of mean is 0.3902 rather than what is shown there 0.5172.

It stated the formula for standard error of means in this website ( http://support.minitab.com/en-us/minitab-express/1/help-and-how-to/modeling-statistics/anova/how-to/two-way-anova/methods-and-formulas/methods-and-formulas/#se-mean ) but not sure how to replicate it

[Star Strider]

The Minitab page is somewhat lacking in the details of how it calculates the mean square error. The degrees-of-freedom in the denominator of that calculation are important, and the page doesn’t mention that little detail.

The Statistics and Machine Learning Toolbox implementation of the two-way ANOVA is the anova2 (link) function. You might find more information there. I recommend Snedecor and Cochran Statistical Methods as a reference.

[crixus]

Hello, thanks for the reply, i will look into that. Appreciate it

[crixus]

Anyway, I finally got how to calculate it. Thanks for you help anyway. Appreciate it.

[Star Strider]

My pleasure.

Answer 2

[Liam Walsh]

To summarize the discussion above, it seems like you are looking to replicate the two-way ANOVA example in Minitab, and get some standard error estimates for the mean. You can do this my making use of the anova2 function or the anova object. Below is an example on how to use the object, which contains a display with several standard quantities in ANOVA including the mean squares value, along with properties and object methods that can be used to examine other quantities in the analysis:

% Load sample data
load popcorn.mat
brand = [repmat("Gourmet",6,1);repmat("National",6,1);repmat("Generic",6,1)];
poppertype = [repmat("Air",3,1);repmat("Oil",3,1);repmat("Air",3,1);repmat("Oil",3,1);repmat("Air",3,1);repmat("Oil",3,1)];
factors = {brand,poppertype};

% Create anova object and show the display, which contains the mean squares
% values
aov = anova(factors,popcorn(:),FactorNames=["Brand" "PopperType"])

aov = 
2-way anova, constrained (Type III) sums of squares.

Y ~ 1 + Brand + PopperType

                  SumOfSquares    DF    MeanSquares     F       pValue  
                  ____________    __    ___________    ___    __________

    Brand            15.75         2       7.875        63         1e-07
    PopperType         4.5         1         4.5        36    3.2548e-05
    Error             1.75        14       0.125                        
    Total               22        17                                    


  Properties, Methods

% Get a table containing the mean squares values
tbl = stats(aov)

tbl = 4×5 table
                  SumOfSquares    DF    MeanSquares     F       pValue  
                  ____________    __    ___________    ___    __________

    Brand            15.75         2       7.875        63         1e-07
    PopperType         4.5         1         4.5        36    3.2548e-05
    Error             1.75        14       0.125                        
    Total               22        17                                    

% To get a similar table without the object, you can use anova2
anova2(popcorn, 3)

ans = 1×3

0.0000 0.0001 0.7462

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